Problem: Given $ m \angle QPR = 4x + 96$, and $ m \angle RPS = 4x + 12$, find $m\angle QPR$. $P$ $Q$ $S$ $R$
Explanation: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Since $\angle QPS$ is a straight angle, we know ${m\angle QPS = 180}$ Substitute in the expressions that were given for each measure: $ {4x + 96} + {4x + 12} = {180}$ Combine like terms: $ 8x + 108 = 180$ Subtract $108$ from both sides: $ 8x = 72$ Divide both sides by $8$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $m\angle QPR$ $ m\angle QPR = 4({9}) + 96$ Simplify: $ {m\angle QPR = 36 + 96}$ So ${m\angle QPR = 132}$.